On the Choice of Design for a Unipolar Alternating-Current Generator

G. A. Sipailov, A. D. Chesalin

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

In order to intensify the production processes of melting and to improve the quality of metals, electromagnetic stirring of the melt is used. For induction stirring, two- or three-phase inductors are used, supplied with low-frequency current \((0.3 \div 1.5\ \text{Hz})\) from converter installations consisting of 8–10 machines. With a sufficiently high output voltage of the converter installations \((120 \div 230\ \text{V})\), the inductor windings have to be made of thin tubes with a large number of turns. Direct water cooling of such windings is difficult because of large hydraulic losses and the danger of accidents due to clogging of the channels.

Unipolar alternating-current generators (UG) make it possible to obtain low-frequency currents of high magnitude and to provide smooth frequency control over a wide range. The low output voltage of a UG will make it possible to reduce the number of turns in the winding of the stirrer inductor and to increase the cross section of the copper tubes of the winding, which will reduce the cost of manufacturing the stator, decrease hydraulic losses in it, and reduce accident hazards associated with water cooling. In addition, the use of a UG will make it possible to reduce the number of machines in converter installations [1].

To solve the stated problems, it is necessary to develop and study alternating-current UGs.

In the present work, the most expedient design of an alternating-current UG is selected on the basis of an analysis of data known in the technical literature, and the basic principles for their calculation are given.

In [1] it was proposed to use, as an alternating-current UG, a direct-current UG excited by an alternating current of low frequency on the order of \(1\text{–}2\ \text{Hz}\). This proposal was justified by the fact that at low frequencies the losses in the steel of a massive magnetic system would be small. Indeed, if at a frequency of \(50\ \text{Hz}\) for a massive magnetic system the specific losses in the steel per unit surface are \(\Delta p = 0.735\ \text{kW}/\text{m}^2\), then at a frequency of \(1\ \text{Hz}\), \(\Delta p = 0.104\ \text{kW}/\text{m}^2\), and at a frequency of \(0.1\ \text{Hz}\), \(\Delta p = 0.033\ \text{kW}/\text{m}^2\). The calculation was made for an induction \(B = 1.4\ \text{T}\) according to the expressions given in [2].

However, it should be borne in mind that in a massive magnetic core an alternating magnetic flux propagates in a surface layer whose dimensions depend on the depth of penetration of the magnetic field. For example, for the steel of a turbogenerator rotor, the depth of penetration of the magnetic field at a frequency of \(50\ \text{Hz}\) is \(\Delta = 0.00167\ \text{m}\), and at a frequency of \(1\ \text{Hz}\), \(\Delta = 0.0116\ \text{m}\),

at a frequency of \(0.1\) Hz—\(\Delta = 0.037\) m. In practice, it may be assumed that at a depth of \(3\Delta\) the magnetic induction is equal to zero. Therefore, it does not appear possible to manufacture an alternating-current UG with a massive magnetic system at powers of hundreds of kW, such as are required for supplying the inductors of agitators. In addition, a massive magnetic system of both the stator and the rotor will constitute, for the excitation magnetic flux, short-circuited turns in which currents of transformer emf will flow, damping the main flux. Consequently, lamination of the magnetic system of the stator and rotor is necessary both in order to distribute the magnetic flux uniformly in the magnetic core and in order to eliminate currents of transformer emf, even for frequencies on the order of \(0.1\)—\(1\) Hz.

The following data may be cited for the thickness of sheets from which magnetic cores can be laminated at low frequencies: at a frequency of \(1\) Hz the sheet thickness is \(3\)—\(5\) mm; for a frequency of \(0.1\) Hz, \(10\)—\(12\) mm.

Alternating-current UGs may be of disk and cylindrical design. One may judge the advantages of one or the other embodiment, in view of the present absence of studies on alternating-current unipolar machines (UM), from the results of analysis of descriptions of inventions [3] and by being guided by investigations carried out for direct-current UMs [4].

It is known [4] that a disk-type direct-current UM has a considerably greater relative weight than a cylindrical one. This ratio will evidently also hold for alternating-current machines. With the greater weight of steel in a disk UM, the losses due to eddy currents and hysteresis will be greater on alternating current. The energy for these losses in a UM is consumed from the circuit of the excitation winding, which will lead to a reduction in the amplification factor of the machine. The magnetic core of an alternating-current UM must be laminated, with the sheets arranged in planes passing through the axis of the machine. It is very difficult to carry out such lamination of the rotor of a disk UM while ensuring sufficient mechanical strength of the disk rotor. It is therefore recommended that the rotor be made of a nonmagnetic electrically conducting material in the form of a split disk, constituting a wheel with spokes without an outer rim. The division of the rods of such a rotor at the outer diameter of the disk is carried out in order to eliminate currents due to transformer emfs, which would arise in the presence of a continuous ring. Making the rotor of nonmagnetic material will lead to a considerable increase in the nonmagnetic gap of the magnetic core and, consequently, to an increase in the dimensions of the excitation winding and of the entire machine.

The laminated rotor of a cylindrical alternating-current UM is structurally simpler in comparison with a disk one. The armature winding of the cylindrical machine consists of rods placed in the slots of the laminated rotor, and is structurally similar to the squirrel cage of an induction motor. Outside the magnetic circuit the rods are connected by a short-circuiting ring, and inside the machine they are brought out to a peculiar commutator consisting of sectors insulated from one another. The division of the rods inside the machine eliminates the short-circuited ring for currents of transformer emf. By selecting the configuration of the rods of the armature winding it is possible to ensure the optimum value of the calculated air gap and, correspondingly, of the excitation winding.

For these reasons, the cylindrical embodiment of an alternating-current UG is preferable. In principle, the design of a cylindrical alternating-current UG is analogous to the design of a cylindrical direct-current UG. However, operation on alternating current entails a number of special features.

Since the armature-winding bars inside the machine are disconnected from one another, the number of simultaneously operating bars is determined by the design of the current-collecting apparatus and depends on the number of collection zones in the zonal current collector. When the number of collection zones is reduced, the number of simultaneously operating bars decreases. In addition, when the brush in a zonal current collector passes from one bar to another, commutation phenomena associated with interruption of the full current will occur, causing pulsations in the output-voltage curve. Designing the armature winding, and, if necessary, also the compensating winding, according to the scheme proposed by P. Claudy [5] will reduce the commutation phenomena associated with interruptions of the full current and will make it possible to reduce the number of collection zones of the zonal current collector while all the bars of the armature winding operate simultaneously.

Since the magnetic circuit of an ac unipolar generator must be laminated, and the lamination must be carried out in planes passing through the machine axis, the question arises of the structural design and of ensuring sufficient mechanical strength of the rotor. A cylindrical rotor (Fig. 1, a) can be glued together from wedge-shaped blocks (Fig. 1, b). At frequencies on the order of 1 Hz, the blocks can be replaced by wedge-shaped plates (Fig. 1, c). Adhesives, for example epoxy-resin-based ones, are currently widely used in industry and ensure sufficient strength of metal joints. However, the mechanical strength and reliability of a laminated rotor will depend in many respects on the technological process of bonding. Therefore, additional measures are required to ensure rotor reliability, for example the installation of bands. In order to avoid the formation of short-circuited turns, the band must be made of insulating material. The use of an insulating band will lead to an increase in the design air gap and, consequently, to an increase in the power consumed by the excitation winding. This can be avoided by making the generator rotor with rotor enlargements (Fig. 2).

Fig. 1. a. Design diagram of a cylindrical ac unipolar generator with a smooth rotor: 1 — compensating winding, 2 — armature winding, 3 — rotor, 4 — continuous current collector, 5 — stator, 6 — zonal current collector, 7 — excitation winding.

Fig. 2. Design diagram of a cylindrical alternating-current UG with rotor projections:
1 — stator pole, 2 — compensating winding, 3 — armature winding, 4 — rotor, 5 — rotor projection, 6 — continuous current collector, 7 — stator yoke, 8 — zonal current collector, 9 — excitation winding

The rotor projections, being the load-bearing part for the armature winding, will at the same time mechanically fasten the radially laminated rotor. The rotor projections are assembled from stamped rings, in which there are slots for the armature-winding bars. Each ring has one radial cut to eliminate a short-circuited turn. During assembly of the rotor projection, the rings are laid so that the cuts are uniformly distributed around the circumference of the rotor projection, and are tightened with studs. For large dimensions, the rotor projection may be assembled from individual segments, laying them in overlap, similarly to the rim of a hydrogenerator rotor.

The stator of a cylindrical alternating-current UG may be made of U-shaped plates assembled into packets, the arrangement of which is shown in Fig. 1, a. Slots for the compensating winding must be provided in the poles of the stator packets. The number of stator packets is evidently related to the number of current-collector zones inside the machine, since the latter must be located in the spaces between the packets in order to ensure access to them during operation. Therefore the number of stator packets will be determined by design considerations. The excitation winding, as in a direct-current UM, is made in the form of one or several cylindrical coils located between the stator poles. The stator poles of an alternating-current UG may also be made in the form of cylindrical rings, manufactured analogously to the rotor projections and pressed into the bores of the stator-yoke packets (Fig. 2). The stator packets are laminated from individual plates and fastened to the machine frame.

Thus, a cylindrical alternating-current UG may be made with rotor projections and without them. By analogy with a direct-current UG, it is evident that the relative weight of a UG with a smooth rotor will be less than the relative weight of a UG with rotor projections for identical armature currents and peripheral speeds. But the rotor with rotor projections will be more reliable. The feasibility of one or another rotor design can be assessed more precisely as a result of the development and investigation of prototypes.

The calculation of a cylindrical alternating-current UG may be carried out using the basic calculation relations given by B. L. Alievskii in [6], taking into account the particular features of the execution of the armature winding according to the sche-

... by P. Claudi [5]. The basic design equation of a cylindrical alternating-current UG has the form

\[ D=\sqrt[3]{\frac{P_{\mathrm{e}}}{\sigma \lambda n}}, \tag{1} \]

where \(D\) is the rotor diameter (the diameter of the rotor enlargement for a UG with rotor enlargements), m; \(P_{\mathrm{e}}\) is the electromagnetic power of the generator, kVA; \(\sigma\) is the generator utilization coefficient, \(\dfrac{\mathrm{kVA}}{m^{3}\cdot \mathrm{rev}/\mathrm{s}}\); \(\lambda\) is the design coefficient; \(n\) is the rotor speed, rev/s.

With a compensating winding, the armature emf under load may be taken as equal to the no-load emf, whose rms value is

\[ E=2.22\,D l B_{m\delta} n, \tag{2} \]

where \(l\) is the active length of the rotor per pole, m; \(B_{m\delta}\) is the amplitude value of the magnetic induction in the air gap, T.

Since the armature winding is made according to P. Claudi’s scheme, the number of simultaneously operating bars of the armature winding will not depend on the number of brushes of the zonal current collection and will be equal to the total number of winding bars \(N\). Then, for a bar cross section \(q_c\) and a current density in it \(j_{\mathrm{a}}\), the rms value of the armature current is

\[ I_{\mathrm{a}}=N I_c=N q_c j_{\mathrm{a}}. \tag{3} \]

where \(I_{\mathrm{a}}=q_c j_{\mathrm{a}}\) is the current in a bar.

Hence the linear loading of the generator is

\[ A=\frac{I_{\mathrm{a}}}{\pi D}=\frac{N I_c}{\pi D} \tag{4} \]

and the electromagnetic power, taken as the design value, is

\[ P_{\mathrm{e}}=E I_{\mathrm{a}}\cdot 10^{-3}. \tag{5} \]

The expression for the design coefficient \(\lambda\) of a cylindrical UG with a smooth rotor is given in [6]. For a UG with rotor enlargements,

\[ \lambda=0.25\,\frac{B_{m r}}{B_{m\delta}}\left(D_p^{*2}-d_{\mathrm{v}}^{*2}\right), \tag{6} \]

where \(B_{m r}\) is the amplitude value of the magnetic induction in the rotor;

\[ D_p^*=\frac{D_p}{D}; \qquad d_{\mathrm{v}}^*=\frac{d_{\mathrm{v}}}{D}; \]

\(D\) is the diameter of the rotor enlargement; \(D_p\) is the rotor diameter; \(d_{\mathrm{v}}\) is the shaft diameter.

To carry out further investigations on the basis of the relations presented, a prototype of a compensated cylindrical alternating-current UG with rotor enlargements and half utilization of the active length of the rotor was developed and built for a current of 6300 A at an output voltage of 0.9 V.

On the basis of the analysis performed, it may be concluded that an alternating-current UG must be made with a laminated magnetic system. Among the known versions and designs of alternating-current UGs, the cylindrical version should be regarded as the most acceptable, as it is for direct-current UGs.

References

1. Ya. I. Drobinin, T. Ya. Drobinina. A unipolar alternating-current generator. Proceedings of UPI, collection no. 156, 1967.

2. I. A. Syromyatnikov. Operating Modes of Synchronous Generators. Gosenergoizdat, 1952.

3. G. A. Sipaylov, A. D. Chesalin. Unipolar alternating-current electrical machines. In: Low-Power Electric-Power-Supply and Electric-Drive Devices, vol. 2, Energiya Publishing House, 1970.

4. A. I. Bertinov, B. L. Alievsky, S. R. Troitsky. Unipolar Electrical Machines with a Liquid-Metal Current Collector. Energiya Publishing House, 1966.

5. P. Klaudy. Unipolarmaschine für Wechselstrom. Austrian patent no. 210514, class 21 d, 85, 1960.

6. B. L. Alievsky. Low-frequency unipolar alternating-current generators for supplying devices for induction stirring of molten metals. Proceedings of the Conference on Unipolar Electrical Machines, Energiya Publishing House, 1969.